Simplify the following expression and state the condition under which the simplification is valid. You can assume that $n \neq 0$. $p = \dfrac{n(n + 5)}{8n} \div \dfrac{8(n + 5)}{-8} $
Explanation: Dividing by an expression is the same as multiplying by its inverse. $p = \dfrac{n(n + 5)}{8n} \times \dfrac{-8}{8(n + 5)} $ When multiplying fractions, we multiply the numerators and the denominators. $p = \dfrac{ n(n + 5) \times -8 } { 8n \times 8(n + 5) } $ $ p = \dfrac{-8n(n + 5)}{64n(n + 5)} $ We can cancel the $n + 5$ so long as $n + 5 \neq 0$ Therefore $n \neq -5$ $p = \dfrac{-8n \cancel{(n + 5})}{64n \cancel{(n + 5)}} = -\dfrac{8n}{64n} = -\dfrac{1}{8} $